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Smallest and Largest Values? (Part 1)

Here's the same task, but with a different twist now:

Here's the same task, but with a different twist now:

Fill in the input boxes on the left to create a valid setup so that angle ACB is ACUTE and ANGLE ACB is as SMALL AS POSSIBLE.

What is the value of the smallest possible value you got for ? Why can't it be any smaller than this?

Fill in the input boxes on the left to create a valid setup so that angle ACB is ACUTE and ANGLE ACB is as LARGE AS POSSIBLE.

What is the value of the largest possible value you got for ? Why can't it be any larger than this?